Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.9597)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 4 and fixed z

For fixed z and a=-23/4, b>=a

For fixed z and a=-23/4, b=5/4

http://functions.wolfram.com/07.23.03.9597.01

Input Form

Hypergeometric2F1[-(23/4), 5/4, 5/2, z] == (1/(3364725 Pi^(3/2) z^(3/2))) (4 (2 (-201894 + 706629 z - 2931691 z^2 + 5562655 z^3 - 6019155 z^4 + 3819392 z^5 - 1329152 z^6 + 196608 z^7) EllipticE[(1/2) (1 - Sqrt[z])] - 2 (-201894 + 706629 z - 2931691 z^2 + 5562655 z^3 - 6019155 z^4 + 3819392 z^5 - 1329152 z^6 + 196608 z^7) EllipticE[(1/2) (1 + Sqrt[z])] - (-201894 - 100947 Sqrt[z] + 706629 z - 496279 z^(3/2) - 2931691 z^2 + 1082935 z^(5/2) + 5562655 z^3 - 1281885 z^(7/2) - 6019155 z^4 + 868880 z^(9/2) + 3819392 z^5 - 318464 z^(11/2) - 1329152 z^6 + 49152 z^(13/2) + 196608 z^7) EllipticK[(1/2) (1 - Sqrt[z])] + (-201894 + 100947 Sqrt[z] + 706629 z + 496279 z^(3/2) - 2931691 z^2 - 1082935 z^(5/2) + 5562655 z^3 + 1281885 z^(7/2) - 6019155 z^4 - 868880 z^(9/2) + 3819392 z^5 + 318464 z^(11/2) - 1329152 z^6 - 49152 z^(13/2) + 196608 z^7) EllipticK[(1/2) (1 + Sqrt[z])]) Gamma[3/4]^2)

Standard Form

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MathML Form

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type='integer'> 6019155 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 1281885 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 7 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 5562655 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 1082935 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 5 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2931691 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 496279 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 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Rule Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]